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Closed-Form Approximations for Optimal (r, q) and (S, T) Policies in a Parallel Processing Environment

Authors :
Hanqin Zhang
Marcus Ang
Karl Sigman
Jing-Sheng Jeannette Song
Source :
Operations Research. 65:1414-1428
Publication Year :
2017
Publisher :
Institute for Operations Research and the Management Sciences (INFORMS), 2017.

Abstract

We consider a single-item continuous-review (r, q) inventory system with a renewal demand process and independent, identically distributed stochastic lead times. Using a stationary marked-point process technique and a heavy-traffic limit, we prove a previous conjecture that inventory position and inventory on-order are asymptotically independent. We also establish closed-form expressions for the optimal policy parameters and system cost in heavy-traffic limit, the first of their kind, to our knowledge. These expressions sharpen our understanding of the key determinants of the optimal policy and their quantitative and qualitative impacts. For example, the results demonstrate that the well-known square-root relationship between the optimal order quantity and demand rate under a sequential processing environment is replaced by the cube root under a stochastic parallel processing environment. We further extend the study to periodic-review (S, T) systems with constant lead times. The electronic companion is available at https://doi.org/10.1287/opre.2017.1623 .

Details

ISSN :
15265463 and 0030364X
Volume :
65
Database :
OpenAIRE
Journal :
Operations Research
Accession number :
edsair.doi...........a8f3066a7dcd4c2c5eeee6d253644b55
Full Text :
https://doi.org/10.1287/opre.2017.1623